4  Walkability

This analysis considers local walkability by calculating travel times to the closest public playground. Playgrounds are a useful candidate to assess the potential of walking to a nearby amenity as they are distributed evenly through the city with an average catchment of 600m (Figure 4.1).

Figure 4.1: Locations of council playgrounds designed with a 600m catchment.

4.1 Distance and speed on hilly terrain

Distance-based planning is easy and objective. However, it doesn’t translate well to people’s decision making which are typically time-centric and, account for the 5Cs of walkability [1]. Hence, even simple distance to time conversions can be more informative to the layperson planning a walking trip to the park. Figure 4.2 shows a conversion from distance to time assuming a speed of 5km/h - a common conversion based on a fit adult e.g. Section 3.4 in NZTA pedestrian planning and design guide.

Figure 4.2: Walkability maps coloured as both distance (m) and time (minutes).

As expected, the histograms of distance and time with a linear conversion look the same with the time variant being more useful for comparison with an upcoming trip - much like typical Google map direction checks.

4.2 Accounting for hills

While Tobler’s function for calculating speed given a hill gradient is rather old, it is still the best option available when real world data is not available for re-parametrisation. Tobler’s hiking function for speed, ν\nu, is a shifted exponential with three parameters aa, bb and cc which give the fastest speed, speed retardation due to gradient and shift from zero respectively.

ν=aexp(−b|slope+c|) \nu = a \exp^{(-b|slope + c|)}

Note that slopeslope in the equation is a dimensionless quantity: dhdx\frac{dh}{dx} (or, rise / run). Terminology-wise, slopeslope, is equivalent to gradient and inclination. Similarly, speed is given in in km/h and can be converted to a travel time in minutes with a multiplicative factor, (60/1000). Both time and speed versions of Tobler’s function are shown in the graph below.

Figure 4.3: Tobler’s function parameters from original paper [2] and Chris Brunsdon’s form with parameters fitted with Strava data [3].

Figure 4.4 shows how speed by hill gradient converts to travel time by hill gradient. Flat curves for 3km/h and 5km/h are shown for reference. Both Tobler’s and Brundon’s curves are skewed - with the highest speeds for negative gradients (i.e. while walking downhill). Tobler’s parameters correspond to a 5km/h speed at zero gradient.

Figure 4.4: Visualisation of Tobler’s functional form as time and speed using parameters from original paper and Chris Brunsdon’s form with parameters fitted with Strava data

4.3 Differences due to hills

While the Wellington City Council (WCC) plans playgrounds based on distance, the presence of hills can increase travel times considerably. Heatmaps are useful for a holistic picture but lack connection to the average citizen’s day to day life. A simple Bayesian model of average walking times and spread in walking times for the suburb connects citizens better to their expected walking times as well as how suitable their neighbourhoods are for walking.

Figure 4.5: Forest plot showing average (μ\mu) and spread (σ\sigma) in walking time to the nearest playground.